Triangle JKL is reflected across the y-axis to create ∆J' K' L' . Are the two figures are congruent

[tex]20^{\tfrac 52}\\\\=(20^5)^{\tfrac 12}\\\\=\left(20^4 \cdot 20 \right)^{\tfrac 12}\\\\=20^{\tfrac 42} \cdot 20^{\tfrac 12}\\\\=20^2 \sqrt{20}\\\\=400\sqrt{4 \times 5}\\\\=400 \times 2\sqrt 5\\\\=800\sqrt 5[/tex]

Answer:

[tex]800\sqrt{5}[/tex]

Step-by-step explanation:

Given: [tex]\large (20)^\text{$ \dfrac{5}{2} $}[/tex]

Properties of Exponents:

Rational Exponent Property: [tex]\large x^\text{$ \dfrac{m}{n} $} = \large \text{$ \sqrt[n]{x^m} $}[/tex]

Product of Powers Property:

1. Convert into a radical:

[tex]\sqrt[2]{20^5} \implies \sqrt{20^5}[/tex]

2. Simplify the expression:

[tex]\sqrt{20^2\times20^2\times20^1}\\\\\implies \sqrt{20^4\times20}\\\\\implies 20^2\sqrt{20}\\\\\implies 20^2\sqrt{4\times5}\\\\\implies 20^2\times2\sqrt{5}[/tex]

3. Evaluate the power:

[tex]20\times20\times2\sqrt{5}\\\\\implies 400\times2\sqrt{5}[/tex]

4. Multiply:

[tex](400\times2)\sqrt{5}\\\\\implies800\sqrt{5}[/tex]

Answer:

13

Step-by-step explanation:

a parallelogram has sides that are parallel to the opposite side. This means that y + 7 is going to be parallel to 20.

Two opposing sides of a parallelogram are parallel and equal

You know that the length of both of the sides is equivalent because the other set of opposing lines is also parallel (you can think of it as cutting off the line segment of y+7 and 20 at the same length. )

this means that we can set up the equation to find y as:

y + 7 = 20

then, you can proceed to find y by isolating it:

y + 7 = 20 ; so therefore

y + 7    =    20

   - 7           -7

y           =     13

y = 13

So, the value of y is 13

The value of the next term in the geometric sequence is 16

From the graph, we have the following highlights:

The means that:

Next term = Current term * 2

From the graph, we have:

Current term = 8

So, the equation becomes

Next term = 8 * 2

Evaluate

Next term = 16

Hence, the value of the next term in the geometric sequence is 16

Read more about geometric sequence at:

https://brainly.com/question/24643676

#SPJ1

Answer:

Perimeter=150cm

Step-by-step explanation:

25cm×6=150cm

Answer:

h'(z) = 2

Step-by-step explanation:

(b) First, let's expand everything so our equation is easier to look at.
h(z) = (3-4)(8-2z+3)
         (-1)(-2z+11)
         2z-11

Now, let's find the derivative:
h'(z) = 2

Answer:

B

Step-by-step explanation:

We can either use sine or cosine, I choose cosine but sine works the same. cos(angle) = adj/hyp. adj = cos(angle) x hyp. adj = cos(30)8, cos(30) = √3/2. √3/2 x 8 = 4√3

Answer:

D.

Step-by-step explanation:

Use Quadratic formula

x =  [-b +- sqrt (b^2 - 4ac) ]  / 2a     with a = 6   b = -24    c = 1

  to find

         x = 2 ± sqrt (23/6)

Answer:

D

Step-by-step explanation:

The model rocket was 600 feet above the ground at 4.5 seconds and 12 seconds.

"It is a diagram that represents data in an organized manner."

"It is the height of the object above the surface of the ground."

For given question,

The graph shows the altitude, in feet, of a model rocket t seconds after launch.

From the graph we can observe that the model rocket was 600 feet above the ground at 4.5 seconds and 12 seconds.

Therefore, the model rocket was 600 feet above the ground at 4.5 seconds and 12 seconds.

Learn more about the graph of the function here:

https://brainly.com/question/12700952

#SPJ3

Answer:

47.1408

Step-by-step explanation:

They gave us the percentage of a number and wants us to find the whole

to do that we will use the following equation:

46.116*100/4.5 = 47.1408 is the number we are looking for.

Answer:

y= -1/5x+5

STEP BY STEP EXPLAINATION:

m = slope = -1/5

c = y-intercept = 5

equation of a straight line:

y=mx+c

so.

y= -1/5x+5

8.57 liters glucose (in liters) is needed for 30 units of blood.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

For 7 units of blood = 2 l of glucose needed.

Foe 1 units of blood, glucose needed = 2/7

For, 30 units of blood , glucose needed = 8.57 liters

Hence, 8.57 liters glucose (in liters) is needed for 30 units of blood.

Learn more about unitary method here:

https://brainly.com/question/22056199

#SPJ1

Answer:

x=1

Step-by-step explanation:

4x=4

(Linear equation)

Solved:-

Transpose 4 from LHS to RHS:

[tex] \rm = > x = \tt \cfrac{4}{4} [/tex]

[tex] \rm = > x = \tt1 [/tex]

Answer:

55.2 is the mean

Explanation:

Given data set:  {113, 14, 23, 12, 114}

Mean = sum of the terms/number of terms

Mean = (113 + 14 + 23 + 12 + 114)/5

          = (276)/5

          = 55.2

Answer:

Mean = 55.2

Step-by-step explanation:

Given data set:   113, 14, 23, 12, 114

To find the mean of a data set, divide the sum of all data values by the total number of data values:

[tex]\large \begin{aligned}\sf Mean & = \sf\dfrac{sum\:of\:all\:data\:values}{total\:number\:of\:data\:values} \\\\\implies \sf Mean & = \sf \dfrac{113 + 14 + 23 + 12 + 114}{5}\\\\& = \sf \dfrac{276}{5}\\\\& = \sf 55.2\end{aligned}[/tex]

The patient would be administered 4 tablets per dose.

In mathematics, solving word problems involves a careful understanding of the content of the problem. This will enable the use of appropriate variables and data representation.

From the given information:

From the standard conversion rate, we know that:

Here, to determine the number of dose to be administered, we have:

(x) /dose = 1000 mg/250 mg

x = 4 dose.

Learn more about word problems here:

https://brainly.com/question/745684

#SPJ1

Answer:

Step-by-step explanation:

The ratio of boys to girls in a school is 4:5. There are 220 boys in the school. How many students attend the school?​

find the number of girls

4 : 5 = 220 : x

x = 5 * 220 : 4

x = 275

sum boys and girls

220 + 275 =

495 (your answer)

check

4 : 5 = 220 : 275

4 : 5 = 4 : 5

the answer is good

Answer:

25%

Step-by-step explanation:

percent = part/whole × 100%

percent = 9/36 × 100%

percent = 25%

Answer:

25%

Step-by-step explanation:

If you divide 36 by 9 you get 4.  If you do the same for 100, and divide by four, you get 25.  Therefore, 9 is 25% of 36.

The function f(x) = 2x -14 is a polynomial function

The equation of the function is given as:

f(x) = 2x -14

A polynomial is represented as:

f(x) =ax^n + bx^(n - 1)....... + c

Where n is at least 1.

The function f(x) = 2x -14 is a polynomial with a degree of 1

Hence, the function f(x) = 2x -14 is a polynomial function

Read more about polynomial function at:

https://brainly.com/question/20896994

#SPJ1

Answer:

45

Step-by-step explanation:

1/3 of 90

= 1/3 * 90

= 90/3

= 30

Let the missing number be x.

2/3 of x

= 2/3 * x

= 2x/3

30 = 2x/3

Cross multiply,

2x = 30 * 3

2x = 90

x = 90/2

x = 45

Hence,

the missing number is 45.

Answer: 6:1

Step-by-step explanation:

Answer:

4,186.67 in³

Step-by-step explanation:

V = (4/3)πr³

V = (4/3)(3.14)(10 in)³

V = (4/3)(3.14)(1,000 in³)

V = 4,186.666667 in³

Answer:

The representative sample contained more girls than boys.

Step-by-step explanation:

Since there is roughly 1.5x more girls than boys, the sample size will likely contain more girls than boys when chosen at random.

Option d is the correct answer. All real numbers are greater than or equal to 2.

Domain of a function--The domain of the function is the set or collection of all the x-values for which the function is well defined.

Range of a function--The range of a function is the set of all the values which are attained by a function in its defined domain.

By looking at the graph we observe that the function is continuously increasing and the function takes all the real values greater than as well as equal to 2( since there is a closed circle at (1,2). Hence, the range is: [2,∞).

Thus Option d is the correct answer. All real numbers are greater than or equal to 2.

To know more about domain and range follow

https://brainly.com/question/2264373

#SPJ1

Based on the calculations, the area of the shaded region is equal to 22 square foot.

By critically observing the geometric shapes, the area of the shaded region can be calculated by using this formula:

Area of shaded region = Area of square - Area of circle.

Note: The diameter of this circle is equal to the side length of the square because the circumference of this circle lies on the circumference of the square.

Radius = diameter/2 = 10/2 = 5 feet.

For the area of square, we have:

Area of square = S²

Area of square = 10²

Area of square = 100 square foot.

For the area of circle, we have:

Area of circle = πr²

Area of circle = 3.14 × 5²

Area of circle = 78.5 square foot.

Substituting the parameters into the formula, we have;

Area of shaded region = Area of square - Area of circle.

Area of shaded region = 100 - 78.5

Area of shaded region = 21.5 ≈ 22

Area of shaded region = 22 square foot.

Read more on area of circle here: https://brainly.com/question/2278809

#SPJ1

Find the area to the nearest square foot of the shaded region below, consisting of a square with a circle cut out of it. Use 3.14 as an approximation for π.

The angle (off of a north-south line) at which a navy carrier needs to travel to sail straight to the submarine is 53.843°.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite the 90° angle.

The Navy carrier, Mercy, is sailing in the Pacific Ocean. The ship is in the sea, 4,365 miles south of a city. On radar, they notice a submarine is 7,390 miles away from them and north-west of their current position.

Therefore, the angle at which the Carrier needs to move to reach the submarine is,

Cosθ = 4365/7390

θ = Cos⁻¹ (0.59)

θ = 53.843°

Hence, the angle (off of a north-south line) at which a navy carrier needs to travel to sail straight to the submarine is 53.843°.

Learn more about Trigonometric functions:

https://brainly.com/question/6904750

#SPJ1

Using the equation of the proportional relationship:

Average rate of speed = 60

Time taken to go 300 miles = 5 hrs

Distance travelled in 2.5 hrs = 150 miles

A equation of a proportional relationship models the relationship between two variables, x and y, that has a constant of k. It is expressed as y = kx.

Given the following:

Equation: d = 60t

d = distance in miles

t = time in hours

Average rate of speed for the bus = k = 60

Time (t) it would take to go 300 miles (d):

300 = 60(t)

300/60 = t

t = 5 hours

Distance (d) it would travel in 2.5 hours (t):

d = 60(2.5)

d = 150 miles

Learn more about the equation of a proportional relationship on:

https://brainly.com/question/6869319

#SPJ1

15

Percentages represent a proportion of a number. There are 2 ways to find a percent of a whole number.

Multiple of 10

Since 30% is a multiple of 10%, there is a shortcut we can use. We can find 10% and then multiply by 3 in order to find 30%. First, find 10% of 50. Like always, 10% of any number is that number divided by 10 (move the decimal 1 place to the left).

So, 10% of 50 is 5.0.

Then, to find 30%, multiply 5 by 3.

30% of 50 is 15.

Multiplication

The more consistent method includes multiplication, this can be used with any percentage. To use this method we need to convert 30% to a decimal. To convert any percentage to a decimal divide by 100 (move the decimal 2 places to the left).

Now, we can multiply this decimal by the whole number, 50. This will give us our desired answer.

So, this once again shows that 30% of 50 is 15.